Local regime-switching models are a natural consequence of combining the concept of a local volatility model with that of a regime-switching model. However, there are two main challenges in the calibration of local regime-switching models; a) the determination of the volatility function for each state involves all the state prices whereas only one market price is available, and b) it is not clear on how to accurately and efficiently determine local volatility functions, even when the state prices are all given.

In this talk, a closed system for option pricing and data extraction under the classical regime-switching model is firstly proposed with a special approach, splitting one market price into “market-implied state prices”. Based on this framework, two different numerical algorithms are designed after transforming the target problem into optimal control problems. The accuracy and stability of the newly designed algorithms are shown through synthetic tests, and their performance with the involvement of real market data have been further demonstrated using options written on the S&P 500 index.